Kinematic models of interseismic deformation from inversion of GPS and InSAR measurements to estimate fault parameters and coupling degree

We have used kinematic models in two Italian regions to reproduce surface interseismic velocities obtained from InSAR and GPS measurements. We have considered a Block modeling, BM, approach to evaluate which fault system is actively accommodating the occurring deformation in both considered areas. We have performed a study for the Umbria-Marche Apennines, obtaining that the tectonic extension observed by GPS measurements is explained by the active contribution of at least two fault systems, one of which is the Alto Tiberina fault, ATF. We have estimated also the interseismic coupling distribution for the ATF using a 3D surface and the result shows an interesting correlation between the microseismicity and the uncoupled fault portions. The second area analyzed concerns the Gargano promontory for which we have used jointly the available InSAR and GPS velocities. Firstly we have attached the two datasets to the same terrestrial reference frame and then using a simple dislocation approach, we have estimated the best fault parameters reproducing the available data, providing a solution corresponding to the Mattinata fault. Subsequently we have considered within a BM analysis both GPS and InSAR datasets in order to evaluate if the Mattinata fault may accommodate the deformation occurring in the central Adriatic due to the relative motion between the North-Adriatic and South-Adriatic plates. We obtain that the deformation occurring in that region should be accommodated by more that one fault system, that is however difficult to detect since the poor coverage of geodetic measurement offshore of the Gargano promontory. Finally we have performed also the estimate of the interseismic coupling distribution for the Mattinata fault, obtaining a shallow coupling pattern. Both of coupling distributions found using the BM approach have been tested by means of resolution checkerboard tests and they demonstrate that the coupling patterns depend on the geodetic data positions.

Implications of regional fault distribution and kinematics for the uplift of rift flanks around the Rwenzori Mountains, Southwestern Uganda

Das Ziel dieser Arbeit bestand in der Untersuchung der Störungsverteilung und der Störungskinematik im Zusammenhang mit der Hebung der Riftschultern des Rwenzori Gebirges.rnDas Rwenzori Gebirge befindet sich im NNE-SSWbis N-S verlaufenden Albertine Rift, des nördlichsten Segments des westlichen Armes des Ostafrikanischen Grabensystems. Das Albertine Rift besteht aus Becken unterschiedlicher Höhe, die den Lake Albert, Lake Edward, Lake George und Lake Kivu enthalten. Der Rwenzori horst trennt die Becken des Lake Albert und des Lake Edward. Es erstreckt sich 120km in N-S Richtung, sowie 40-50km in E-W Richtung, der h¨ochste Punkt befindet sich 5111 ü. NN. Diese Studie untersucht einen Abschnitt des Rifts zwischen etwa 1°N und 0°30'S Breite sowie 29°30' und 30°30' östlicher Länge ersteckt. Auch die Feldarbeit konzentrierte sich auf dieses Gebiet.rnrnHauptzweck dieser Studie bestand darin, die folgende These auf ihre Richtigkeit zu überprüfen: ’Wenn es im Verlauf der Zeit tatsächlich zu wesentlichen Änderungen in der Störungskinematik kam, dann ist die starke Hebung der Riftflanken im Bereich der Rwenzoris nicht einfach durch Bewegung entlang der Graben-Hauptst¨orungen zu erklären. Vielmehr ist sie ein Resultat des Zusammenspiels mehrerer tektonische Prozesse, die das Spannungsfeld beeinflussen und dadurch Änderungen in der Kinematik hervorrufen.’ Dadurch konzentrierte sich die Studie in erster Linie auf die Störungsanalyse.rnrnDie Kenntnis regionaler Änderungen der Extensionsrichtung ist entscheidend für das Verständnis komplexer Riftsysteme wie dem Ostafrikanischen Graben. Daher bestand der Kern der Untersuchung in der Kartierung von Störungen und der Untersuchung der Störungskinematik. Die Aufnahme strukturgeologischer Daten konzentrierte sich auf die Ugandische Seite des Rifts, und Pal¨aospannungen wurden mit Hilfe von St¨orungsdaten durch Spannungsinversion rekonstruiert.rnDie unterschiedliche Orientierung spr¨oder Strukturen im Gelände, die geometrische Analyse der geologischen Strukturen sowie die Ergebnisse von Mikrostrukturen im Dünnschliff (Kapitel 4) weisen auf verschiedene Spannungsfelder hin, die auf mögliche Änderungen der Extensionsrichtung hinweisen. Die Resultate der Spannungsinversion sprechen für Ab-, Über- und Blattverschiebungen sowie für Schrägüberschiebungen (Kapitel 5). Aus der Orientierung der Abschiebungen gehen zwei verschiedene Extensionsrichtungen hervor: im Wesentlichen NW-SE Extension in fast allen Gebieten, sowie NNE-SSW Extension im östlichen Zentralbereich.rnAus der Analyse von Blattverschiebungen ergaben sich drei unterschiedliche Spannungszustände. Zum Einen NNW-SSE bis N-S Kompression in Verbindung mit ENE-WSW bzw E-W Extension wurde für die nördlichen und die zentralen Ruwenzoris ausgemacht. Ein zweiter Spannungszustand mit WNW-ESE Kompression/NNE-SSW Extension betraf die Zentralen Rwenzoris. Ein dritter Spannungszustand mit NNW-SSE Extension betraf den östlichen Zentralteil der Rwenzoris. Schrägüberschiebungen sind durch dazu schräge Achsen charakterisiert, die für N-S bis NNW-SSE Kompression sprechen und ausschließlich im östlichen Zentralabschnitt auftreten. Überschiebungen, die hauptsächlich in den zentralen und den östlichen Rwenzoris auftreten, sprechen für NE-SW orientierten σ2-Achsen und NW-SE Extension.rnrnEs konnten drei unterschiedliche Spannungseinflüsse identifiziert werden: auf die kollisionsbedingte Bildung eines Überschiebungssystem folgte intra-kratonische Kompression und schließlich extensionskontrollierte Riftbildung. Der Übergang zwischen den beiden letztgenannten Spannungszuständen erfolgte Schrittweise und erzeugte vermutlich lokal begrenzte Transpression und Transtension. Gegenw¨artig wird die Störungskinematik der Region durch ein tensiles Spannungsregime in NW-SE bis N-S Richtung bestimmt.rnrnLokale Spannungsvariationen werden dabei hauptsächlich durch die Interferenzrndes regionalen Spannungsfeldes mit lokalen Hauptst¨orungen verursacht. Weitere Faktoren die zu lokalen Veränderungen des Spannungsfeldes führen können sind unterschiedliche Hebungsgeschwindigkeiten, Blockrotation oder die Interaktion von Riftsegmenten. Um den Einfluß präexistenter Strukturen und anderer Bedingungen auf die Hebung der Rwenzoris zu ermitteln, wurde der Riftprozeß mit Hilfe eines analogen ’Sandbox’-Modells rekonstruiert (Kapitel 6). Da sich die Moho-Diskontinuität im Bereich des Arbeitsgebietes in einer Tiefe von 25 km befindet, aktive Störungen aber nur bis zu einer Tiefe von etwa 20 km beobachtet werden können (Koehn et al. 2008), wurden nur die oberen 25 km im Modell nachbebildet. Untersucht und mit Geländebeobachtungen verglichen wurden sowohl die Reihenfolge, in der Riftsegmente entstehen, als auch die Muster, die sich im Verlauf der Nukleierung und des Wachstums dieser Riftsegmente ausbilden. Das Hauptaugenmerk wurde auf die Entwicklung der beiden Subsegmente gelegt auf denen sich der Lake Albert bzw. der Lake Edward und der Lake George befinden, sowie auf das dazwischenliegende Rwenzori Gebirge. Das Ziel der Untersuchung bestand darin herauszufinden, in welcher Weise das südwärts propagierende Lake Albert-Subsegment mit dem sinistral versetzten nordwärts propagierenden Lake Edward/Lake George-Subsegment interagiert.rnrnVon besonderem Interesse war es, in welcherWeise die Strukturen innerhalb und außerhalb der Rwenzoris durch die Interaktion dieser Riftsegmente beeinflußt wurden. rnrnDrei verschiedene Versuchsreihen mit unterschiedlichen Randbedingungen wurden miteinander verglichen. Abhängig vom vorherrschenden Deformationstyp der Transferzone wurden die Reihen als ’Scherungs-dominiert’, ’Extensions-dominiert’ und als ’Rotations-dominiert’ charakterisiert. Die Beobachtung der 3-dimensionalen strukturellen Entwicklung der Riftsegmente wurde durch die Kombination von Modell-Aufsichten mit Profilschnitten ermöglicht. Von den drei genannten Versuchsreihen entwickelte die ’Rotationsdominierten’ Reihe einen rautenförmiger Block im Tranferbereich der beiden Riftsegmente, der sich um 5−20° im Uhrzeigersinn drehte. DieserWinkel liegt im Bereich des vermuteten Rotationswinkel des Rwenzori-Blocks (5°). Zusammengefasst untersuchen die Sandbox-Versuche den Einfluss präexistenter Strukturen und der Überlappung bzw. Überschneidung zweier interagierender Riftsegmente auf die Entwicklung des Riftsystems. Sie befassen sich darüber hinaus mit der Frage, welchen Einfluss Blockbildung und -rotation auf das lokale Stressfeld haben.

Understanding block rotation of strike-slip fault zones: Paleomagnetic and structural approach

This thesis is focused on the paleomagnetic rotation pattern inside the deforming zone of strike-slip faults, and the kinematics and geodynamics describing it. The paleomagnetic investigation carried out along both the LOFZ and the fore-arc sliver (38º-42ºS, southern Chile) revealed an asymmetric rotation pattern. East of the LOFZ and adjacent to it, rotations are up to 170° clockwise (CW) and fade out ~10 km east of fault. West of the LOFZ at 42ºS (Chiloé Island) and around 39°S (Villarrica domain) systematic CCW rotations have been observed, while at 40°-41°S (Ranco-Osorno domain) and adjacent to the LOFZ CW rotations reach up to 136° before evolving to CCW rotations at ~30 km from the fault. These data suggest a directed relation with subduction interface plate coupling. Zones of high coupling yield to a wide deforming zone (~30 km) west of the LOFZ characterized by CW rotations. Low coupling implies a weak LOFZ and a fore-arc dominated by CCW rotations related to NW-sinistral fault kinematics. The rotation pattern is consistent with a quasi-continuous crust kinematics. However, it seems unlikely that the lower crust flux can control block rotation in the upper crust, considering the cold and thick fore-arc crust. I suggest that rotations are consequence of forces applied directly on both the block edges and along the main fault, within the upper crust. Farther south, at the Austral Andes (54°S) I measured the anisotropy of magnetic susceptibility (AMS) of 22 Upper Cretaceous to Upper Eocene sites from the Magallanes fold-thrust belt internal domains. The data document continuous compression from the Early Cretaceous until the Late Oligocene. AMS data also show that the tectonic inversion of Jurassic extensional faults during the Late Cretaceous compressive phase may have controlled the Cenozoic kinematic evolution of the Magallanes fold-thrust belt, yielding slip partitioning.

Fault detection, diagnosis and active fault tolerant control for a satellite attitude control system

Modern control systems are becoming more and more complex and control algorithms more and more sophisticated. Consequently, Fault Detection and Diagnosis (FDD) and Fault Tolerant Control (FTC) have gained central importance over the past decades, due to the increasing requirements of availability, cost efficiency, reliability and operating safety. This thesis deals with the FDD and FTC problems in a spacecraft Attitude Determination and Control System (ADCS). Firstly, the detailed nonlinear models of the spacecraft attitude dynamics and kinematics are described, along with the dynamic models of the actuators and main external disturbance sources. The considered ADCS is composed of an array of four redundant reaction wheels. A set of sensors provides satellite angular velocity, attitude and flywheel spin rate information. Then, general overviews of the Fault Detection and Isolation (FDI), Fault Estimation (FE) and Fault Tolerant Control (FTC) problems are presented, and the design and implementation of a novel diagnosis system is described. The system consists of a FDI module composed of properly organized model-based residual filters, exploiting the available input and output information for the detection and localization of an occurred fault. A proper fault mapping procedure and the nonlinear geometric approach are exploited to design residual filters explicitly decoupled from the external aerodynamic disturbance and sensitive to specific sets of faults. The subsequent use of suitable adaptive FE algorithms, based on the exploitation of radial basis function neural networks, allows to obtain accurate fault estimations. Finally, this estimation is actively exploited in a FTC scheme to achieve a suitable fault accommodation and guarantee the desired control performances. A standard sliding mode controller is implemented for attitude stabilization and control. Several simulation results are given to highlight the performances of the overall designed system in case of different types of faults affecting the ADCS actuators and sensors.

NLGA based Active Control in Aerospace: fault tolerability, disturbance rejection, and parameter estimation

A new control scheme has been presented in this thesis. Based on the NonLinear Geometric Approach, the proposed Active Control System represents a new way to see the reconfigurable controllers for aerospace applications. The presence of the Diagnosis module (providing the estimation of generic signals which, based on the case, can be faults, disturbances or system parameters), mean feature of the depicted Active Control System, is a characteristic shared by three well known control systems: the Active Fault Tolerant Controls, the Indirect Adaptive Controls and the Active Disturbance Rejection Controls. The standard NonLinear Geometric Approach (NLGA) has been accurately investigated and than improved to extend its applicability to more complex models. The standard NLGA procedure has been modified to take account of feasible and estimable sets of unknown signals. Furthermore the application of the Singular Perturbations approximation has led to the solution of Detection and Isolation problems in scenarios too complex to be solved by the standard NLGA. Also the estimation process has been improved, where multiple redundant measuremtent are available, by the introduction of a new algorithm, here called "Least Squares - Sliding Mode". It guarantees optimality, in the sense of the least squares, and finite estimation time, in the sense of the sliding mode. The Active Control System concept has been formalized in two controller: a nonlinear backstepping controller and a nonlinear composite controller. Particularly interesting is the integration, in the controller design, of the estimations coming from the Diagnosis module. Stability proofs are provided for both the control schemes. Finally, different applications in aerospace have been provided to show the applicability and the effectiveness of the proposed NLGA-based Active Control System.

Tecniche di fault tolerance in swarm robotics

Questa tesi presenta e discute le sfide per ottenere sistemi di swarm robotis affidabili e tolleranti ai guasti e quindi anche alcuni metodi per rilevare anomalie in essi, in modo tale che ipotetiche procedure per il recupero possano essere affrontate, viene sottolineata inoltre l’ importanza di un’ analisi qualitativa dei guasti.

Design di un sistema di fault detection per un'architettura fail-safe di attuazione delle superfici di controllo di un UAV

In questo lavoro di tesi si affronta una delle problematiche che si presentano oggi nell'impiego degli APR (Aeromobili a Pilotaggio Remoto): la gestione della safety. Non si può più, in altri termini, negare che tali oggetti siano parte integrante dello spazio aereo civile. Proprio su questo tema recentemente gli enti regolatori dello spazio aereo stanno proiettando i loro sforzi al fine di stabilire una serie di regolamenti che disciplinino da una parte le modalità con cui questi oggetti si interfacciano con le altre categorie di velivoli e dall'altra i criteri di idoneità perché anche essi possano operare nello spazio aereo in maniera sicura. Si rende quindi necessario, in tal senso, dotare essi stessi di un sufficiente grado di sicurezza che permetta di evitare eventi disastrosi nel momento in cui si presenta un guasto nel sistema; è questa la definizione di un sistema fail-safe. Lo studio e lo sviluppo di questa tipologia di sistemi può aiutare il costruttore a superare la barriera oggi rappresentata dal regolamento che spesso e volentieri rappresenta l'unico ostacolo non fisico per la categoria dei velivoli unmanned tra la terra e il cielo. D'altro canto, al fine di garantire a chi opera a distanza su questi oggetti di avere, per tutta la durata della missione, la chiara percezione dello stato di funzionamento attuale del sistema e di come esso può (o potrebbe) interagire con l'ambiente che lo circonda (situational awarness), è necessario dotare il velivolo di apparecchiature che permettano di poter rilevare, all'occorrenza, il malfunzionamento: è questo il caso dei sistemi di fault detection. Questi due fondamentali aspetti sono la base fondante del presente lavoro che verte sul design di un ridotto ma preponderante sottosistema dell'UAV: il sistema di attuazione delle superfici di controllo. Esse sono, infatti, l'unico mezzo disponibile all'operatore per governare il mezzo nelle normali condizioni di funzionamento ma anche l'ultima possibilità per tentare di evitare l'evento disastroso nel caso altri sottosistemi siano chiaramente fuori dalle condizioni di normale funzionamento dell'oggetto.

Determination of Pelvic Orientation from Ultrasound Images Using Patch-SSMs and a Hierarchical Speed of Sound Compensation Strategy

In the field of computer assisted orthopedic surgery (CAOS) the anterior pelvic plane (APP) is a common concept to determine the pelvic orientation by digitizing distinct pelvic landmarks. As percutaneous palpation is - especially for obese patients - known to be error-prone, B-mode ultrasound (US) imaging could provide an alternative means. Several concepts of using ultrasound imaging to determine the APP landmarks have been introduced. In this paper we present a novel technique, which uses local patch statistical shape models (SSMs) and a hierarchical speed of sound compensation strategy for an accurate determination of the APP. These patches are independently matched and instantiated with respect to associated point clouds derived from the acquired ultrasound images. Potential inaccuracies due to the assumption of a constant speed of sound are compensated by an extended reconstruction scheme. We validated our method with in-vitro studies using a plastic bone covered with a soft-tissue simulation phantom and with a preliminary cadaver trial.

Can imagined whole-body rotations improve vestibular compensation?

Unilateral damage to the labyrinth and the vestibular nerve cause rotational vertigo, postural imbalance, oculomotor disorders and spatial disorientation. Electrophysiological investigations in animals revealed that such deficits are partly due to imbalanced spontaneous activity and sensitivity to motion in neurons located in the ipsilesional and contralesional vestibular nuclei. Neurophysiological reorganizations taking place in the vestibular nuclei are the basis of the decline of the symptoms over time, a phenomenon known as vestibular compensation. Vestibular compensation is facilitated by motor activity and sensory experience, and current rehabilitation programs favor physical activity during the acute stage of a unilateral vestibular loss. Unfortunately, vestibular-defective patients tend to develop strategies in order to avoid movements causing imbalance and nausea (in particular body movements towards the lesioned side), which impedes vestibular compensation. Neuroanatomical evidence suggests a cortical control of postural and oculomotor reflexes based on corticofugal projections to the vestibular nuclei and, therefore, the possibility to manipulate vestibular functions through top-down mechanisms. Based on evidence from neuroimaging studies showing that imagined whole-body movements can activate part of the vestibular cortex, we propose that mental imagery of whole-body rotations to the lesioned and to the healthy side will help rebalancing the activity in the ipsilesional and contralesional vestibular nuclei. Whether imagined whole-body rotations can improve vestibular compensation could be tested in a randomized controlled study in such patients beneficiating, or not, from a mental imagery training. If validated, this hypothesis will help developing a method contributing to reduce postural instability and falls in vestibular-defective patients. Imagined whole-body rotations thus could provide a simple, safe, home-based and self-administered therapeutic method with the potential to overcome the inconvenience related to physical movements.

Integrated Geophysical Investigation of the St. James Fault Complex: A Case Study

We noninvasively detected the characteristics and location of a regional fault in an area of poor bedrock exposure complicated by karst weathering features in the subsurface. Because this regional fault is associated with sinkhole formation, its location is important for hazard avoidance. The bedrock lithologies on either side of the fault trace are similar; hence, we chose an approach that capitalized on the complementary strengths of very low frequency (VLF) electromagnetic, resistivity, and gravity methods. VLF proved most useful as a first-order reconnaissance tool, allowing us to define a narrow target area for further geophysical exploration. Fault-related epikarst was delineated using resistivity. Ultimately, a high-resolution gravity survey and subsequent inverse modeling using the results of the resistivity survey helped to further constrain the location and approximate orientation of the fault. The combined results indicated that the location of the fault trace needed to be adjusted 53 m south of the current published location and was consistent with a north-dipping thrust fault. Additionally, a gravity low south of the fault trace agreed with the location of conductive material from the resistivity and VLF surveys. We interpreted these anomalies to represent enhanced epikarst in the fault footwall. We clearly found that a staged approach involving a progression of methods beginning with a reconnaissance VLF survey, followed by high-resolution gravity and electrical resistivity surveys, can be used to characterize a fault and fault-related karst in an area of poor bedrock surface exposure.

Compensability index for compensation radiotherapy after treatment interruptions

Background The goal of our work was to develop a simple method to evaluate a compensation treatment after unplanned treatment interruptions with respect to their tumour- and normal tissue effect. Methods We developed a software tool in java programming language based on existing recommendations to compensate for treatment interruptions. In order to express and visualize the deviations from the originally planned tumour and normal tissue effects we defined the compensability index. Results The compensability index represents an evaluation of the suitability of compensatory radiotherapy in a single number based on the number of days used for compensation and the preference of preserving the originally planned tumour effect or not exceeding the originally planned normal tissue effect. An automated tool provides a method for quick evaluation of compensation treatments. Conclusions The compensability index calculation may serve as a decision support system based on existing and established recommendations.

FPGA BASED DESIGN FOR ACCELERATED FAULT-TESTING OF INTEGRATED CIRCUITS

In the past few decades, integrated circuits have become a major part of everyday life. Every circuit that is created needs to be tested for faults so faulty circuits are not sent to end-users. The creation of these tests is time consuming, costly and difficult to perform on larger circuits. This research presents a novel method for fault detection and test pattern reduction in integrated circuitry under test. By leveraging the FPGA's reconfigurability and parallel processing capabilities, a speed up in fault detection can be achieved over previous computer simulation techniques. This work presents the following contributions to the field of Stuck-At-Fault detection: We present a new method for inserting faults into a circuit net list. Given any circuit netlist, our tool can insert multiplexers into a circuit at correct internal nodes to aid in fault emulation on reconfigurable hardware. We present a parallel method of fault emulation. The benefit of the FPGA is not only its ability to implement any circuit, but its ability to process data in parallel. This research utilizes this to create a more efficient emulation method that implements numerous copies of the same circuit in the FPGA. A new method to organize the most efficient faults. Most methods for determinin the minimum number of inputs to cover the most faults require sophisticated softwareprograms that use heuristics. By utilizing hardware, this research is able to process data faster and use a simpler method for an efficient way of minimizing inputs.

Compensation, Incentives and Risk: Economic Theory and Russian Practise

Mr. Pechersky set out to examine a specific feature of the employer-employee relationship in Russian business organisations. He wanted to study to what extent the so-called "moral hazard" is being solved (if it is being solved at all), whether there is a relationship between pay and performance, and whether there is a correlation between economic theory and Russian reality. Finally, he set out to construct a model of the Russian economy that better reflects the way it actually functions than do certain other well-known models (for example models of incentive compensation, the Shapiro-Stiglitz model etc.). His report was presented to the RSS in the form of a series of manuscripts in English and Russian, and on disc, with many tables and graphs. He begins by pointing out the different examples of randomness that exist in the relationship between employee and employer. Firstly, results are frequently affected by circumstances outside the employee's control that have nothing to do with how intelligently, honestly, and diligently the employee has worked. When rewards are based on results, uncontrollable randomness in the employee's output induces randomness in their incomes. A second source of randomness involves the outside events that are beyond the control of the employee that may affect his or her ability to perform as contracted. A third source of randomness arises when the performance itself (rather than the result) is measured, and the performance evaluation procedures include random or subjective elements. Mr. Pechersky's study shows that in Russia the third source of randomness plays an important role. Moreover, he points out that employer-employee relationships in Russia are sometimes opposite to those in the West. Drawing on game theory, he characterises the Western system as follows. The two players are the principal and the agent, who are usually representative individuals. The principal hires an agent to perform a task, and the agent acquires an information advantage concerning his actions or the outside world at some point in the game, i.e. it is assumed that the employee is better informed. In Russia, on the other hand, incentive contracts are typically negotiated in situations in which the employer has the information advantage concerning outcome. Mr. Pechersky schematises it thus. Compensation (the wage) is W and consists of a base amount, plus a portion that varies with the outcome, x. So W = a + bx, where b is used to measure the intensity of the incentives provided to the employee. This means that one contract will be said to provide stronger incentives than another if it specifies a higher value for b. This is the incentive contract as it operates in the West. The key feature distinguishing the Russian example is that x is observed by the employer but is not observed by the employee. So the employer promises to pay in accordance with an incentive scheme, but since the outcome is not observable by the employee the contract cannot be enforced, and the question arises: is there any incentive for the employer to fulfil his or her promises? Mr. Pechersky considers two simple models of employer-employee relationships displaying the above type of information symmetry. In a static framework the obtained result is somewhat surprising: at the Nash equilibrium the employer pays nothing, even though his objective function contains a quadratic term reflecting negative consequences for the employer if the actual level of compensation deviates from the expectations of the employee. This can lead, for example, to labour turnover, or the expenses resulting from a bad reputation. In a dynamic framework, the conclusion can be formulated as follows: the higher the discount factor, the higher the incentive for the employer to be honest in his/her relationships with the employee. If the discount factor is taken to be a parameter reflecting the degree of (un)certainty (the higher the degree of uncertainty is, the lower is the discount factor), we can conclude that the answer to the formulated question depends on the stability of the political, social and economic situation in a country. Mr. Pechersky believes that the strength of a market system with private property lies not just in its providing the information needed to compute an efficient allocation of resources in an efficient manner. At least equally important is the manner in which it accepts individually self-interested behaviour, but then channels this behaviour in desired directions. People do not have to be cajoled, artificially induced, or forced to do their parts in a well-functioning market system. Instead, they are simply left to pursue their own objectives as they see fit. Under the right circumstances, people are led by Adam Smith's "invisible hand" of impersonal market forces to take the actions needed to achieve an efficient, co-ordinated pattern of choices. The problem is that, as Mr. Pechersky sees it, there is no reason to believe that the circumstances in Russia are right, and the invisible hand is doing its work properly. Political instability, social tension and other circumstances prevent it from doing so. Mr. Pechersky believes that the discount factor plays a crucial role in employer-employee relationships. Such relationships can be considered satisfactory from a normative point of view, only in those cases where the discount factor is sufficiently large. Unfortunately, in modern Russia the evidence points to the typical discount factor being relatively small. This fact can be explained as a manifestation of aversion to risk of economic agents. Mr. Pechersky hopes that when political stabilisation occurs, the discount factors of economic agents will increase, and the agent's behaviour will be explicable in terms of more traditional models.